Your impression is correct. But the problem is due to the orthodontics tilting the lower teeth too far forward thereby reducing the 'overjet' and limiting the amount the lower jaw can move forward. Do not have the upper jaw advancement with your nose/lip angle or it will not look positive!....
I have performed over 4000 of your type of necessary procedures, (orthognathic surgery).I would have to see you in person but I would probably recommend maxillary advancement with mild mandibular setback
The need for genioplasty after those procedures would have to be assessed at that time and...
The downgrading of your maxilla will of course lengthen your face exactly by the number of mm downgrafted. It is simple math. Likewise a lenghrhenig Genioplasty will do the same and will lengthen the lower 1/3 of your face from the lip commissure downward and it will stretch your skin as you asked.